Set-builder notation

Definition

Set-builder notation is a mathematical shorthand used to describe a set by stating the properties that its members must satisfy. It is often used to specify domains and ranges of functions.

5 Must Know Facts For Your Next Test

1. Set-builder notation uses the format $\{ x \mid \text{condition} \}$, where $x$ is an element of the set and the condition describes a property of $x$.
2. It can represent both finite and infinite sets.
3. Inequalities are frequently used within set-builder notation to define ranges for functions.
4. Set-builder notation is useful for describing intervals on the real number line, such as $\{ x \mid 1 \leq x < 5 \}$.
5. The condition inside the set-builder notation can include multiple constraints, such as $\{ x \mid x > 2 \text{ and } x \leq 10 \}$.

Review Questions

• What is the purpose of using set-builder notation?
• How would you write the set of all real numbers greater than or equal to -3 in set-builder notation?
• Explain how you would use set-builder notation to describe the domain of a function with inequality constraints.

Related terms

Inequality: A mathematical statement that compares two values or expressions using inequality symbols like $<$, $>$, $\leq$, or $\geq$.

Domain: The set of all possible input values (usually $x$) for which a function is defined.

Range: The set of all possible output values (usually $y$) that a function can produce based on its domain.